CN109978902B - Automatic extraction method for center line of irregular banded target - Google Patents
Automatic extraction method for center line of irregular banded target Download PDFInfo
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Abstract
The invention discloses an automatic extraction method of an irregular banded target center line, which is characterized by comprising the following steps of: s1, disassembling a banded target; s2, enhancing a linear structure; s3, extracting a central line based on multiple regression; s4, communicating the center lines, recovering the topological connectivity of the strip-shaped target, and realizing the automatic extraction of the center line of the irregular strip-shaped target. The method has the advantages that a set of multi-scale polynomial filters and a binary banded target are designed to carry out convolution operation, so that the linear characteristic of the banded target is enhanced, and the regularity of irregular banded targets is realized; the problem of center line extraction is converted into the research of the quantitative relation of discrete points in the x direction and the y direction, and the center line smooth extraction is realized by using a multivariate self-adaptive regression spline method. The method has high stability, and can accurately and smoothly extract the central line of the irregular banded target.
Description
Technical Field
The invention relates to the technical field of image processing, in particular to an automatic extraction method of an irregular banded target center line, which can be applied to extraction of a binary road image center line, a binary medical image blood vessel center line and drawing of machinery, buildings, water conservancy, municipal administration and the like.
Background
The center line is the simplest way to express the strip-shaped target (such as a binary road skeleton), and the outline information, the topology information and the location information of the strip-shaped target are reserved. How to extract the central line of a strip-shaped object from the strip-shaped object is a common concern in many fields such as biomedicine, mechanical manufacturing, digital image processing and the like.
In recent years, the center line extraction method in the related field can be classified into the following five categories according to the implementation principle: a refinement-based method, a shortest path-based method, a hessel matrix-based method, a fitting-based method, a regression analysis-based method.
(1) A refinement method. (a) The morphological refinement method is the most common method for centerline extraction, and the corresponding algorithms can be divided into two types: firstly, based on a hit-miss transformation method; secondly, the method is based on a Maximal Disk method. But this type of approach can create glitches and unnecessary branching. (b) Topology refinement, also known as "onion peeling" is another commonly used refinement method. And (3) peeling off the outer layer by layer through iteration to finally obtain the central line of the strip-shaped target, wherein the algorithm can keep the geometric and topological characteristics of the strip-shaped target, and the overall connectivity of the strip-shaped target cannot be changed. The algorithm can be used for extracting the central line of a binary band-shaped target and is also suitable for extracting the central line of a 3D image, but huge iterative computation is needed.
(2) Geodesic method. The geodesic method is also a common center line extraction method, obtains a center line by calculating the shortest path at two ends of a binary banded target, has the advantages of high operation speed and no burr phenomenon, and has the defects that: (a) The generated central line is easy to cling to the outer side of the banded target and deviates from the actual central line; (b) the crossover problem cannot be solved.
(3) A method for extracting a ridge line based on a Haisel matrix. The Hassel matrix method can extract the center line of the binaryzation banded target, but the operation amount is huge and the stability is poor. In addition, the method is excessively dependent on the gradient or high-order derivative of the image, is sensitive to noise, and is not good in image extraction effect for low contrast.
(4) Fitting method. The method comprises the steps of firstly setting seed points and then connecting the seed points to form a central line. According to the concrete mode of seed point connection, the method can be further divided into the following steps: a straight line connection method, a B spline curve fitting method, a least square method and the like. The straight line connection method is simple in calculation, but large in error, and suitable for connection of simple strip-shaped targets which are small in curvature and approximate to straight lines, and the distance between seed points is controlled within an error allowable range according to the actual shape of the strip-shaped targets. The shape of the curve fitted by the B-spline is smooth but the positioning error of the seed points cannot be corrected. The least square method can ensure that the total error of the fitted curve and the seed point is minimum, but the effect of fitting the complex strip-shaped target is poor.
(5) And (4) a regression method. The method takes a binary strip-shaped target as a discrete observation point, and converts the problem of extracting a central line from the binary strip-shaped target into the problem of determining the quantitative relation between an abscissa and an ordinate by analyzing the discrete observation point. The method has strong adaptability, the extracted central line is smooth, a new thought is provided for the problem of central line extraction, but the central line of the intersected banded target cannot be directly extracted.
In summary, the existing centerline extraction method is prone to generate defects of burrs or deviations, and when the centerline of an irregular strip-shaped target is extracted, the defects of the existing method are more obvious and sometimes even fail.
Disclosure of Invention
The invention aims to provide an automatic extraction method of an irregular banded target center line, which solves the defect that the existing center line extraction method is easy to generate burrs or deviation and realizes accurate and smooth extraction of the irregular banded target center line.
In order to achieve the purpose, the technical scheme of the invention is as follows: an automatic extraction method for the center line of an irregular strip-shaped target comprises the following steps:
s1 strip target dismantling
S1.1, firstly, performing morphological thinning operation on a banded target to be extracted;
s1.2, acquiring the intersection point of the refined strip-shaped target by adopting a Rutoviz intersection number method, wherein the specific operation is as follows:
defining Rutoviz intersection number N of pixel points P c Is composed of
N i ＝(N 1 ，N 2 ，…，N 9 ) And N is 1 ＝N 9 (1)
N calculated according to formula (1) c Judging the type of the pixel point P when N is c When =1, determining the pixel point P as the end point of the band target; when N is present c When =2, only 2 non-zero pixels N in 8 neighborhoods of the pixel P i 、N j And non-zero pixel point N i 、P、N j Non-colinear, and determining that the pixel point P is a cross point; when N is present c >2, judging that the pixel point P is a cross point of the banded target;
s1.3, disconnecting the banded target at each intersection point, and disassembling the banded target into a plurality of mutually-disjoint linear structures;
s2 linear structure enhancement
Designing a group of multi-scale polynomial filter banks and carrying out convolution operation on a banded target binary image to obtain a pixel set with a linear structure, wherein the polynomial filter banks adopt a short rectangular form and are defined as follows:
in formula (2), w is the width of the rectangle and represents the width of the band-shaped target; l is the length of the long side of the rectangle and is proportional to the value of w; r is a relaxation space, which is a constant related to the boundary of the banded object;
calculating a band-shaped target binary image I by taking the function F (a, w) as a polynomial filter with an angle a and a width w d Convolution with F (a, w) to obtain a linear response image I with an angle a and a width w f (a,w)
I f (a,w)＝|I d *F(a,w)| (3)
Obtaining a group of response image sets by using a plurality of filters with different directions and different widths, and obtaining a result after enhancing a linear structure by calculating the maximum value of corresponding pixel values of all linear response images
I m ＝max a,w I f (a,w) (4)
S3 centerline extraction based on multiple regression
Extracting the central line of the banded target with the enhanced linear structure by adopting a MARS multi-element self-adaptive regression spline method, and outputting a group of continuous output variables
In the formula (5), a 0 For the parameter constant, M represents the number of spline functions, B m (X) is the mth spline function, a m For the coefficients of the mth spline function, a least squares fit may be performed on the data set to obtain a m The combination coefficient of (c):
B m (X) is a generalized linear regression model for MARS, defined specifically as:
in the formula (7), k m Is the number of nodes, S km Spline function representing left and right sides, v (k, m) is the identity of independent variable, t is node, t is km Is the node location; spline function B by using MARS multivariate adaptive regression spline method m (X) is expressed as a set of piecewise functions, as follows:
equation (8) and equation (9) are spline functions to the left and right of the node t, [ (t) km -x)] + And [ (x-t) km )] + A pair of truncated splines at the representation node t;
s4, connecting the central lines and recovering the topological connectivity of the strip-shaped target
And (3) taking the position coordinate of the cross point obtained in the step (S1.2) as a circle center O, taking the pixel R as a radius, and connecting the circle center O with the adjacent central line end point in the search range to realize the automatic extraction of the central line of the irregular banded target.
The invention has the beneficial effects that: the invention designs a novel method for extracting a banded target central line based on linear structure enhancement and multiple regression, which is characterized in that a set of multi-scale polynomial filters and a binary banded target are subjected to convolution operation to enhance the linear characteristics of the banded target and realize the regularity of irregular banded targets; the problem of center line extraction is converted into the research of the quantitative relation of discrete points in the x direction and the y direction, and the center line smooth extraction is realized by using a multivariate self-adaptive regression spline method. The method has high stability, and can accurately and smoothly extract the central line of the irregular band-shaped target.
Drawings
FIG. 1 is a flow chart of the centerline extraction for a band target according to the present invention;
FIG. 2 is a 8-domain structure diagram of a pixel P;
FIG. 3 is a pair of truncated splines from node t;
fig. 4 is a schematic centerline connection.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.
As shown in fig. 1, an automatic extraction method for the center line of an irregular strip-shaped target includes the following steps:
s1 band-shaped target dismantling
Because the regression-based method cannot solve the problem of intersection, the method cannot be directly used for extracting the center line from the banded target, and the banded target needs to be disassembled before the center line is extracted. The specific operation is as follows:
s1.1, firstly, performing morphological thinning operation on a banded target to be extracted;
s1.2, acquiring the intersection point of the refined banded target by adopting a Rutoviz intersection number method, wherein the method specifically comprises the following steps:
defining Rutoviz intersection number N of pixel points P c Is composed of
N i ＝(N 1 ，N 2 ，…，N 9 ) And N is 1 ＝N 9 (1)
As shown in fig. 2, the structure diagram of the 8-neighborhood of the pixel point P. N calculated according to formula (1) c Judging the type of the pixel point P when N is c If =1, determining the pixel point P as an end point of the ribbon target; when N is present c When =2, pixel point P is in 8 neighborhoodsWith only 2 non-zero pixels N i 、N j And non-zero pixel point N i 、P、N j Non-colinear, and determining that the pixel point P is a cross point; when N is present c >2, judging that the pixel point P is a cross point of the banded target;
s1.3, breaking the strip-shaped target at each intersection point position, and disassembling the strip-shaped target into a plurality of mutually-disjoint linear structures.
S2 linear structure enhancement
The linear structure is the most important characteristic of the banded target, and enhancing the linear characteristic blocks and suppressing the nonlinear characteristic blocks of the banded target are effective ways for regulating irregular banded targets. The invention designs a group of multi-scale polynomial filter banks and a banded target binary image to carry out convolution operation to obtain a pixel set with a linear structure, wherein the polynomial filter banks adopt a short rectangular form and are defined as follows:
in formula (2), w is the width of the rectangle and represents the width of the band-shaped target; l is the length of the long side of the rectangle and is proportional to the value of w; r is a relaxation space, a constant related to the band target boundary; the region extents w, r + w are designed to capture the boundary response, so that the template gives the maximum response when correlated with two parallel edges, with pixels with linear structures filling in between the boundaries.
Calculating a band-shaped target binary image I by taking the function F (a, w) as a polynomial filter with an angle a and a width w d Convolution with F (a, w) to obtain a linear response image I with an angle a and a width w f (a,w)
I f (a,w)＝|I d *F(a,w)| (3)
A set of response images is obtained by using a plurality of filters with different widths and different directions, preferably 8 filters with different widths and different directions, and a higher response value indicates a stronger linear structure. Obtaining a result I after the linear structure is enhanced by calculating the maximum value of the corresponding pixel values of all the linear response images m 。
I m ＝max a,w I f (a,w) (4)
S3 centerline extraction based on multiple regression
On the basis of enhancing the linear structure of the banded target and regulating the target form, converting the central line extraction problem into a regression problem. Since the image data file is stored primarily in raster form, the banded object may be viewed as a collection of image raster points, with the coordinates (xi, yi) of each raster being viewed as a discrete observation. The centerline extraction problem can be viewed as exploring the x, y direction interdependent quantitative relationship from a multitude of discrete observations, and regression analysis is an effective method to determine such quantitative relationship. Due to the complex diversity of the banded targets, the traditional user-driven modeling method is difficult to find a proper model to assume and process the complex and diverse variable relation, and a data-driven non-parameter regression method is adopted for solving the problem of centerline extraction.
Based on the analysis, the MARS multivariate adaptive regression spline method adopted by the invention extracts the central line of the banded target after the linear structure is enhanced, and outputs a group of continuous output variables
In the formula (5), a 0 Is a parameter constant, M represents the number of spline functions, B m (X) is the mth spline function, a m For the coefficients of the mth spline function, a least squares fit may be performed on the data set to obtain a m The combination coefficient of (a):
B m (X) is a generalized linear regression model of MARS, defined specifically as:
in the formula (7), k m Is the number of nodes, S km Spline function representing left and right sides, v (k, m) is the identity of independent variable, t is node, t is km Is the node position; spline function B by using MARS multivariate adaptive regression spline method m (X) is expressed as a set of piecewise functions, as follows:
equation (8) and equation (9) are splines to the left and right of node t, [ (t) km -x)] + And [ (x-t) km )] + Representing a pair of truncated splines at node t as shown in figure 3.
S4, communicating the central lines and recovering the topological connectivity of the strip-shaped target
And (3) connecting the center O with the adjacent center line end points (A, B and C) in the search range by taking the position coordinate of the intersection point obtained in the step (S1.2) as the center O and the pixel R as the radius, and realizing the automatic extraction of the center line of the irregular band-shaped target as a center line connection schematic diagram of the center line shown in figure 4.
The above method enhances the regularized band objects by linear structure, on this basis, converts the centerline extraction problem into a regression problem and extracts the centerline by MARS. Compared with the existing method, the method for extracting the center line has high stability, can accurately extract the smooth center line, and has more obvious advantages aiming at the strip-shaped target with an irregular shape.
The described embodiments are only some embodiments of the invention, not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the scope of the present invention.
Claims (1)
1. An automatic extraction method for the central line of an irregular banded target is characterized by comprising the following steps:
s1 band-shaped target dismantling
S1.1, firstly, performing morphological thinning operation on a banded target to be extracted;
s1.2, acquiring the intersection point of the refined banded target by adopting a Rutoviz intersection number method, wherein the method specifically comprises the following steps:
defining Rutoviz intersection number N of pixel point P c Comprises the following steps:
N i ＝(N 1 ，N 2 ，...，N 9 ) And N is 1 ＝N 9 (1)
N calculated according to equation (1) c Judging the type of the pixel point P when N is c When =1, determining the pixel point P as the end point of the band target; when N is present c When the value is not less than 2, only 2 nonzero pixels N are arranged in 8 neighborhoods of the pixel P i 、N j And non-zero pixel point N i 、P、N j Non-collinear, and judging that the pixel point P is a cross point; when N is present c >2, judging that the pixel point P is a cross point of the banded target;
s1.3, disconnecting the banded target at each intersection point, and disassembling the banded target into a plurality of mutually disjoint linear structures;
s2 linear structure enhancement
Designing a group of multi-scale polynomial filter banks and carrying out convolution operation on a banded target binary image to obtain a pixel set with a linear structure, wherein the polynomial filter banks adopt a short rectangular form and are defined as follows:
in formula (2), w is the width of the rectangle and represents the width of the band-shaped target; l is the length of the long side of the rectangle and is proportional to the value of w; r is a relaxation space, a constant related to the band target boundary;
calculating a band-shaped target binary image I by taking the function F (a, w) as a polynomial filter with an angle a and a width w d Convolution with F (a, w) to obtain a linear response image I with an angle a and a width w f (a,w)
I f (a,w)＝|I d *F(a,w)| (3)
Obtaining a group of response image sets by using a plurality of filters with different directions and different widths, and obtaining a result after the linear structure is enhanced by calculating the maximum value of the pixel values corresponding to all the linear response images
I m ＝max a,w I f (a,w) (4)
S3 centerline extraction based on multiple regression
Extracting the central line of the banded target with the enhanced linear structure by adopting a MARS multi-element self-adaptive regression spline method, and outputting a group of continuous output variables
In the formula (5), a 0 For the parameter constant, M represents the number of spline functions, B m (X) is the mth spline function, a m For the coefficients of the mth spline function, a least squares fit may be performed on the data set to obtain a m The combination coefficient of (c):
B m (X) is a generalized linear regression model of MARS, defined specifically as:
in the formula (7), k m Is the number of nodes, S km Spline function representing left and right sides, v (k, m) is the identity of independent variable, t is node, t is km Is the node position; spline function B by using MARS multivariate adaptive regression spline method m (X) is expressed as a set of piecewise functions, specifically as follows:
equation (8) and equation (9) are spline functions to the left and right of the node t, [ (t) km -x)] + And [ (x-t) km )] + A pair of truncated splines at node t;
s4, communicating the central lines and recovering the topological connectivity of the strip-shaped target
And (3) connecting the center O with the adjacent center line end point in the search range by taking the position coordinate of the intersection point obtained in the step (S1.2) as the center O and the pixel R as the radius, so as to realize the automatic extraction of the center line of the irregular band-shaped target.
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| CN101770581A (en) * | 2010-01-08 | 2010-07-07 | 西安电子科技大学 | Semi-automatic detecting method for road centerline in high-resolution city remote sensing image |
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